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3 years ago

5i / 3-4i division of the following

Mathematics

1 answer:

IceJOKER [234]3 years ago

7 0

Answer:

$\frac{5i}{3 - 4i} = \frac{3i - 4}{5}$

Step-by-step explanation:

Given

$\frac{5i}{3 - 4i}$

Required

Solve

We have:

$\frac{5i}{3 - 4i}$

Rationalize

$\frac{5i}{3 - 4i} = \frac{5i}{3 - 4i} * \frac{3 + 4i}{3 + 4i}$

$\frac{5i}{3 - 4i} = \frac{5i(3 + 4i)}{(3 - 4i)(3 + 4i)}$

Apply difference of two squares on the denominator

$\frac{5i}{3 - 4i} = \frac{5i(3 + 4i)}{3^2 - (4i)^2}$

$\frac{5i}{3 - 4i} = \frac{5i(3 + 4i)}{9 - (16*-1)}$

$\frac{5i}{3 - 4i} = \frac{5i(3 + 4i)}{9 +16}$

$\frac{5i}{3 - 4i} = \frac{5i(3 + 4i)}{25}$

Divide common factor (5)

$\frac{5i}{3 - 4i} = \frac{i(3 + 4i)}{5}$

Expand the numerator

$\frac{5i}{3 - 4i} = \frac{3i + 4*-1}{5}$

$\frac{5i}{3 - 4i} = \frac{3i - 4}{5}$

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Given:

The base of 40-foot ladder is 8 feet from the wall.

To find:

How high is the ladder on the wall (round to the nearest foot).

Solution:

Ladder makes a right angle triangle with wall and ground.

We have,

Length of ladder (hypotenuse)= 40 foot

Base = 8 foot

We need to find the perpendicular to get the height of the ladder on the wall.

Let h be the height of the ladder on the wall.

According to the Pythagoras theorem,

$Hypotenuse^2=Base^2+Perpendicular^2$

$(40)^2=(8)^2+(h)^2$

$1600=64+h^2$

$1600-64=h^2$

$1536=h^2$

Taking square root on both sides.

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Height cannot be negative. Round to the nearest foot.

$h\approx 39$

Therefore, the height of the ladder on the wall is 39 foot.

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3 years ago

Mr peterson will buy 80 feet of fencing. The pieces of fence come in whole numbers of feet. His enclosure will be a rectangle an

DIA [1.3K]

The perimeter is:
P = 2x + 2y = 80
The area is:
A = x * y
The area as a function of a variable is:
A (x) = x * (40-x)
Rewriting we have:
A (x) = 40x-x ^ 2
We derive the function:
A '(x) = 40-2x
We equal zero and clear x:
40-2x = 0
2x = 40
x = 40/2
x = 20 feet
The other dimension is:
y = 40 - x
y = 40 - 20
y = 20 feet
The area will be:
A = x * y
A = 20 * 20
A = 400 feet ^ 2
Answer:
The dimensions are:
x = 20 feet
y = 20 feet
The area is:
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Answer:

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Step-by-step explanation:

4(c+2) < 4c + 10

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Subtract 4c from both sides

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